Integrating Jackknife into the Theil-Sen Estimator in Multiple Linear Regression Model

Abstract

In this study, we provide Theil-Sen parameter estimators, which are in multiple linear regression model based on a spatial median, to be examined by the jackknife method. To obtain the proposed estimator, apply the jackknife to a multivariate Theil-Sen estimator (MTSE) from Dang et al. estimators, who proved that the MTSE estimator is asymptotically normal. Robustness, efficiency, and non-normality of the proposed estimator is tested with simulation studies. As a result, the proposed estimator is shown to be robust, consistent, and more efficient in multiple linear regression models with arbitrary error distributions. Also, it is seen that the proposed estimator reduces the effects of outliers even more and gives more reliable results. So, it is clearly observed that the proposed estimator improves the outcome of the multivariate Theil-Sen estimator. In addition, we support with the aid of numerical examples to these results.

Keywords

• jackknife
• robustness
• efficiency
• Theil-Sen estimator
• multiple linear regression
• spatial median